Steady state analysis of a vesicle bioreactor with mechanosensitive channels

Abstract

An intermediate step between simple models of protocells having no membrane structure and the current, complex membrane organization of modern cells considers simple forms of membrane change that interact with the protocell dynamics in predictable ways. Here we analyse a kinetic model of a simple protocell system: a bioreactor vesicle involving mechanosensitive channels. This is a closed lipid bilayer which hosts a minimal metabolism X + E → W + E inside its internal (variable volume) water pool, and with channels anchored in the membrane. The reactor can swell, opening the channels, which in turn allow enhanced passive diffusion of solutes X and W into and out of the reactor. We calculate under what external conditions and parameter regimes the reactor is able to maintain a far from equilibrium steady state, and what behaviours are possible in this reduced complexity scenario. This study is just a preliminary step in modelling the bigger question of how osmotic force sensing devices in early membranes could couple with early metabolisms, enhancing the stability of protocells in changing environments. Bioreactor Kinetic ModelThe bioreactor model (Figure 1) consists of a lipid vesicle floating in a reservoir. The reservoir is assumed so large that solute concentrations exterior to the vesicle are approximately constant. The internal aqueous pool of the vesicle

Emergent Chemical Behavior in Variable-Volume Protocells

“…It can be proven that the individual reactions composing reaction pair Equations (15) and (16) cannot show bistability under any parameter conditions in the CSTR model, nor in the vesicle reactor model (see [ 26 ] and the Supplementary Material ), and therefore, bistability can be claimed as an emergent feature of the system when the two reactions are present together in the low buffer vesicle model. Incidentally, bistability would be lost if a vesicle were to relocate itself to a region of high external buffer concentration.…”

“…One recent semi-empirical study that does pay attention to how finite membrane diffusion rates could limit resources to a compartmentalized proto-metabolism (but within a fixed volume, fixed surface area vesicle) is [ 25 ]. Along the same lines, our own previous work has performed a theoretical analysis of a very simple “bioreactor” consisting of a unimolecular reaction happening inside a vesicle, where the vesicle has again fixed surface area, but now variable volume and mechano-sensitive channels in the membrane [ 26 ]. The vesicle reactor model of the current study is a significant extension of this latter model, further incorporating a first approach to variable vesicle surface area and considering more complex reaction chemistries inside the vesicle reactor.…”